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Solving optimization problems with mean field methods

Peterson, Carsten LU (1993) In Physica A: Statistical Mechanics and its Applications 200(1-4). p.570-580
Abstract

A brief review is given for the use of feed-back artificial neural networks (ANN) to obtain good approximate solutions to combinatorial optimization problems. The key element is the mean field approximation (MFT), which differs from conventional methods and "feels" its ways towards good solutions rather than fully or partly exploring different possible solutions. The methodology, which is illustrated for the graphs bisection and knapsack problems, is easily generalized to Potts systems. The latter is related to the deformable templates method, which is illustrated with the track finding problem. The mean field approximation is based on a variational principle, which also turns out to be very profitable when computing correlations in... (More)

A brief review is given for the use of feed-back artificial neural networks (ANN) to obtain good approximate solutions to combinatorial optimization problems. The key element is the mean field approximation (MFT), which differs from conventional methods and "feels" its ways towards good solutions rather than fully or partly exploring different possible solutions. The methodology, which is illustrated for the graphs bisection and knapsack problems, is easily generalized to Potts systems. The latter is related to the deformable templates method, which is illustrated with the track finding problem. The mean field approximation is based on a variational principle, which also turns out to be very profitable when computing correlations in polymers.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physica A: Statistical Mechanics and its Applications
volume
200
issue
1-4
pages
11 pages
publisher
Elsevier
external identifiers
  • scopus:43949162273
ISSN
0378-4371
DOI
10.1016/0378-4371(93)90562-I
language
English
LU publication?
yes
id
a119de6b-32a3-4ae5-8fb0-ed032d2eac15
date added to LUP
2019-05-14 16:05:15
date last changed
2024-01-01 04:35:34
@article{a119de6b-32a3-4ae5-8fb0-ed032d2eac15,
  abstract     = {{<p>A brief review is given for the use of feed-back artificial neural networks (ANN) to obtain good approximate solutions to combinatorial optimization problems. The key element is the mean field approximation (MFT), which differs from conventional methods and "feels" its ways towards good solutions rather than fully or partly exploring different possible solutions. The methodology, which is illustrated for the graphs bisection and knapsack problems, is easily generalized to Potts systems. The latter is related to the deformable templates method, which is illustrated with the track finding problem. The mean field approximation is based on a variational principle, which also turns out to be very profitable when computing correlations in polymers.</p>}},
  author       = {{Peterson, Carsten}},
  issn         = {{0378-4371}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{1-4}},
  pages        = {{570--580}},
  publisher    = {{Elsevier}},
  series       = {{Physica A: Statistical Mechanics and its Applications}},
  title        = {{Solving optimization problems with mean field methods}},
  url          = {{http://dx.doi.org/10.1016/0378-4371(93)90562-I}},
  doi          = {{10.1016/0378-4371(93)90562-I}},
  volume       = {{200}},
  year         = {{1993}},
}